Abstract
The simultaneous truel is a three-person game which is a generalization of the simple duel. The players' positions are fixed and their firing is simultaneous. Each player's only decision is which of his opponents will be his target. The (simultaneous) firing continues until there is at most one survivor or until all survivors have fired a specified number of times. Each player is assumed to be concerned only with his own survival; he is indifferent to the fate of his opponents. These games (parametrized by the maximum possible number of shots by each player) are examined for equilibrium points. It is found that, in many cases, the truel has a unique equilibrium point at which the player who is the poorest marksman has the greatest chance of survival.
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Kilgour, D.M. The simultaneous truel. Int J Game Theory 1, 229–242 (1971). https://doi.org/10.1007/BF01753447
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DOI: https://doi.org/10.1007/BF01753447